Preprints, Working Papers, ... Year : 2020

Percolation in the Boolean model with convex grains in high dimension

Jean-Baptiste Gouéré

Abstract

We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K ⊂ R d with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or ρK for a further parameter ρ ∈ (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.
Fichier principal
Vignette du fichier
Boolean-model-convex-high-dimension-HAL.pdf (633) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03044355 , version 1 (07-12-2020)

Identifiers

Cite

Jean-Baptiste Gouéré, Florestan Labéy. Percolation in the Boolean model with convex grains in high dimension. 2020. ⟨hal-03044355⟩
215 View
107 Download

Altmetric

Share

More